Two similar wires under the same load yield elongation of $0.1$ $mm$ and $0.05$ $mm$ respectively. If the area of cross- section of the first wire is $4m{m^2},$ then the area of cross section of the second wire is….. $mm^2$

In the Young’s experiment, If length of wire and radius both are doubled then the value of $Y$ will become

A $100\,m$ long wire having cross-sectional area $6.25 \times 10^{-4}\,m ^2$ and Young's modulus is $10^{10}\,Nm ^{-2}$ is subjected to a load of $250\,N$, then the elongation in the wire will be :

$(a)$ A steel wire of mass $\mu $ per unit length with a circular cross section has a radius of $0.1\,cm$. The wire is of length $10\,m$ when measured lying horizontal and hangs from a hook on the wall. A mass of $25\, kg$ is hung from the free end of the wire. Assuming the wire to be uniform an lateral strains $< \,<$ longitudinal strains find the extension in the length of the wire. The density of steel is $7860\, kgm^{-3}$ and Young’s modulus $=2 \times 10^{11}\,Nm^{-2}$.

$(b)$ If the yield strength of steel is $2.5 \times 10^8\,Nm^{-2}$, what is the maximum weight that can be hung at the lower end of the wire ?

A uniform rod of mass $m$, length $L$, area of cross-section $A$ and Young's modulus $Y$ hangs from the ceiling. Its elongation under its own weight will be